cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

A332140 a(n) = 4*(10^(2n+1)-1)/9 - 4*10^n.

Original entry on oeis.org

0, 404, 44044, 4440444, 444404444, 44444044444, 4444440444444, 444444404444444, 44444444044444444, 4444444440444444444, 444444444404444444444, 44444444444044444444444, 4444444444440444444444444, 444444444444404444444444444, 44444444444444044444444444444, 4444444444444440444444444444444
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002278 (4*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332120 .. A332190 (variants with different repeated digit 2, ..., 9).
Cf. A332141 .. A332149 (variants with different middle digit 1, ..., 9).

Programs

  • Maple
    A332140 := n -> 4*((10^(2*n+1)-1)/9-10^n);
  • Mathematica
    Array[4 ((10^(2 # + 1)-1)/9 - 10^#) &, 15, 0]
LinearRecurrence[{111,-1110,1000},{0,404,44044},20] (* Harvey P. Dale, Jul 06 2021 *)
  • PARI
    apply( {A332140(n)=(10^(n*2+1)\9-10^n)*4}, [0..15])
  • Python
    def A332140(n): return (10**(n*2+1)//9-10**n)*4

Formula

a(n) = 4*A138148(n) = A002278(2n+1) - 4*10^n.
G.f.: 4*x*(101 - 200*x)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

A332141 a(n) = 4*(10^(2*n+1)-1)/9 - 3*10^n.

Original entry on oeis.org

1, 414, 44144, 4441444, 444414444, 44444144444, 4444441444444, 444444414444444, 44444444144444444, 4444444441444444444, 444444444414444444444, 44444444444144444444444, 4444444444441444444444444, 444444444444414444444444444, 44444444444444144444444444444, 4444444444444441444444444444444
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002278 (4*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332121 .. A332191 (variants with different repeated digit 2, ..., 9).
Cf. A332140 .. A332149 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332141 := n -> 4*(10^(2*n+1)-1)/9-3*10^n;
  • Mathematica
    Array[4 (10^(2 # + 1)-1)/9 - 3*10^# &, 15, 0]
LinearRecurrence[{111,-1110,1000},{1,414,44144},20] (* or *) Table[ FromDigits[Join[PadRight[{},n,4],{1},PadRight[{},n,4]]],{n,0,20}](* Harvey P. Dale, Aug 17 2020 *)
  • PARI
    apply( {A332141(n)=10^(n*2+1)\9*4-3*10^n}, [0..15])
  • Python
    def A332141(n): return 10**(n*2+1)//9*4-3*10**n

Formula

a(n) = 4*A138148(n) + 1*10^n = A002278(2n+1) - 3*10^n.
G.f.: (1 + 303*x - 700*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

A332143 a(n) = 4*(10^(2*n+1)-1)/9 - 10^n.

Original entry on oeis.org

3, 434, 44344, 4443444, 444434444, 44444344444, 4444443444444, 444444434444444, 44444444344444444, 4444444443444444444, 444444444434444444444, 44444444444344444444444, 4444444444443444444444444, 444444444444434444444444444, 44444444444444344444444444444, 4444444444444443444444444444444
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002278 (4*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332113 .. A332193 (variants with different repeated digit 1, ..., 9).
Cf. A332140 .. A332149 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332143 := n -> 4*(10^(2*n+1)-1)/9-10^n;
  • Mathematica
    Array[4 (10^(2 # + 1)-1)/9 - 10^# &, 15, 0]
  • PARI
    apply( {A332143(n)=10^(n*2+1)\9*4-10^n}, [0..15])
  • Python
    def A332143(n): return 10**(n*2+1)//9*4-10**n

Formula

a(n) = 4*A138148(n) + 3*10^n = A002278(2n+1) - 10^n.
G.f.: (3 + 101*x - 500*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

A332148 a(n) = 4*(10^(2*n+1)-1)/9 + 4*10^n.

Original entry on oeis.org

8, 484, 44844, 4448444, 444484444, 44444844444, 4444448444444, 444444484444444, 44444444844444444, 4444444448444444444, 444444444484444444444, 44444444444844444444444, 4444444444448444444444444, 444444444444484444444444444, 44444444444444844444444444444, 4444444444444448444444444444444
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002278 (4*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332118 .. A332178, A181965 (variants with different repeated digit 1, ..., 9).
Cf. A332140 .. A332149 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332148 := n -> 4*((10^(2*n+1)-1)/9+10^n);
  • Mathematica
    Array[4 ((10^(2 # + 1)-1)/9 + 10^#) &, 15, 0]
  • PARI
    apply( {A332148(n)=(10^(n*2+1)\9+10^n)*4}, [0..15])
  • Python
    def A332148(n): return (10**(n*2+1)//9+10**n)*4

Formula

a(n) = 4*A138148(n) + 8*10^n = A002278(2n+1) + 4*10^n = 4*A332112(n).
G.f.: (8 - 404*x)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

A332142 a(n) = 4*(10^(2*n+1)-1)/9 - 2*10^n.

Original entry on oeis.org

2, 424, 44244, 4442444, 444424444, 44444244444, 4444442444444, 444444424444444, 44444444244444444, 4444444442444444444, 444444444424444444444, 44444444444244444444444, 4444444444442444444444444, 444444444444424444444444444, 44444444444444244444444444444, 4444444444444442444444444444444
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002278 (4*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332112 .. A332192 (variants with different repeated digit 1, ..., 9).
Cf. A332140 .. A332149 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332142 := n -> 4*(10^(2*n+1)-1)/9-2*10^n;
  • Mathematica
    Array[4 (10^(2 # + 1)-1)/9 - 2*10^# &, 15, 0]
  • PARI
    apply( {A332142(n)=10^(n*2+1)\9*4-2*10^n}, [0..15])
  • Python
    def A332142(n): return 10**(n*2+1)//9*4-2*10**n

Formula

a(n) = 4*A138148(n) + 2*10^n = A002278(2n+1) - 2*10^n = 2*A332121(n).
G.f.: (2 + 202*x - 600*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

A332145 a(n) = 4*(10^(2*n+1)-1)/9 + 10^n.

Original entry on oeis.org

5, 454, 44544, 4445444, 444454444, 44444544444, 4444445444444, 444444454444444, 44444444544444444, 4444444445444444444, 444444444454444444444, 44444444444544444444444, 4444444444445444444444444, 444444444444454444444444444, 44444444444444544444444444444, 4444444444444445444444444444444
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002278 (4*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332115 .. A332195 (variants with different repeated digit 1, ..., 9).
Cf. A332140 .. A332149 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332145 := n -> 4*(10^(2*n+1)-1)/9+10^n;
  • Mathematica
    Array[4 (10^(2 # + 1)-1)/9 + 10^# &, 15, 0]
  • PARI
    apply( {A332145(n)=10^(n*2+1)\9*4+10^n}, [0..15])
  • Python
    def A332145(n): return 10**(n*2+1)//9*4+10**n

Formula

a(n) = 4*A138148(n) + 5*10^n = A002278(2n+1) + 10^n.
G.f.: (5 - 101*x - 300*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

A332146 a(n) = 4*(10^(2*n+1)-1)/9 + 2*10^n.

Original entry on oeis.org

6, 464, 44644, 4446444, 444464444, 44444644444, 4444446444444, 444444464444444, 44444444644444444, 4444444446444444444, 444444444464444444444, 44444444444644444444444, 4444444444446444444444444, 444444444444464444444444444, 44444444444444644444444444444, 4444444444444446444444444444444
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002278 (4*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332116 .. A332196 (variants with different repeated digit 2, ..., 9).
Cf. A332140 .. A332149 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332146 := n -> 4*(10^(2*n+1)-1)/9+2*10^n;
  • Mathematica
    Array[4 (10^(2 # + 1)-1)/9 + 2*10^# &, 15, 0]
  • PARI
    apply( {A332146(n)=10^(n*2+1)\9*4+2*10^n}, [0..15])
  • Python
    def A332146(n): return 10**(n*2+1)//9*4+2*10**n

Formula

a(n) = 4*A138148(n) + 6*10^n = A002278(2n+1) + 2*10^n = 2*A332123(n).
G.f.: (6 - 202*x - 200*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

A332147 a(n) = 4*(10^(2*n+1)-1)/9 + 3*10^n.

Original entry on oeis.org

7, 474, 44744, 4447444, 444474444, 44444744444, 4444447444444, 444444474444444, 44444444744444444, 4444444447444444444, 444444444474444444444, 44444444444744444444444, 4444444444447444444444444, 444444444444474444444444444, 44444444444444744444444444444, 4444444444444447444444444444444
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002278 (4*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332117 .. A332197 (variants with different repeated digit 1, ..., 9).
Cf. A332140 .. A332149 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332147 := n -> 4*(10^(2*n+1)-1)/9+3*10^n;
  • Mathematica
    Array[4 (10^(2 # + 1)-1)/9 + 3*10^# &, 15, 0]
LinearRecurrence[{111,-1110,1000},{7,474,44744},20] (* Harvey P. Dale, Mar 08 2022 *)
  • PARI
    apply( {A332147(n)=10^(n*2+1)\9*4+3*10^n}, [0..15])
  • Python
    def A332147(n): return 10**(n*2+1)//9*4+3*10**n

Formula

a(n) = 4*A138148(n) + 7*10^n = A002278(2n+1) + 3*10^n.
G.f.: (7 - 303*x - 100*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
Showing 1-8 of 8 results.

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